1. Technical Field
The present disclosure relates to a control device for a resonant converter.
2. Description of the Related Art
Forced switching converters (switching converters) with devices used for controlling them are known from the state of the art. Resonant converters are a wide range of forced switching converters characterized by the presence of a resonant circuit playing an active role in determining the input-output power flow. In these converters, a bridge (half bridge) consisting of four (two) power switches (typically power MOFSETs) supplied by a direct voltage generates a voltage square wave that is applied to a resonant circuit tuned to a frequency close to the fundamental frequency of said square wave. Thereby, because of the selective features thereof, the resonant circuit mainly responds to the fundamental component and negligibly to the higher-order harmonics of the square wave. As a result, the circulating power may be modulated by changing the frequency of the square wave, holding the duty cycle constant at 50%. Moreover, depending on the resonant circuit configuration, the currents and/or voltages associated with the power flow have a sinusoidal or a piecewise sinusoidal shape.
These voltages are rectified and filtered so as to provide dc power to the load. In offline applications, to comply with safety regulations, the rectification and filtering system supplying the load is coupled to the resonant circuit by a transformer providing the isolation between source and load, required by the above-mentioned regulations. As in all isolated network converters, also in this case a distinction is made between a primary side (as related to the primary winding of the transformer) connected to the input source and a secondary side (as related to the secondary winding(s) of the transformer) providing power to the load through the rectification and filtering system.
Presently, among the many types of resonant converters, the so-called LLC resonant converter is widely used, especially in the half bridge version thereof. The designation LLC comes from the resonant circuit employing two inductors (L) and a capacitor (C); a principle schematic of an LLC resonant converter is shown in FIG. 1. The resonant converter 1 comprises a half bridge of transistors Q1 and Q2 between the input voltage Vin and the ground GND driven by a driving circuit 3. The common terminal HB between the transistors Q1 and Q2 is connected to a circuit block 2 comprising a capacitor Cr, an inductance Ls and another inductance Lp connected in parallel to a transformer 10 with a center-tap secondary. The two windings of the center-tap secondary of transformer 10 are connected to the anodes of two diodes D1 and D2 the cathodes of which are both connected to the parallel of a capacitor Cout and a resistance Rout; the voltage across the parallel Rout, Cout is the output voltage Vout of the resonant converter, while the dc output current lout flows through Rout.
Resonant converters offer considerable advantages as compared to the traditional switching converters (non-resonant converters, typically PWM—Pulse Width Modulation—controlled): waveforms without steep edges, low switching losses in the power switches due to the “soft” switching thereof, high conversion efficiency (>95% is easily reachable), ability to operate at high frequencies, low EMI (Electro Magnetic Interference) generation and, ultimately, high power density (i.e., enabling to build conversion systems capable of handling considerable power levels in a relatively small space).
As in most dc-dc converters, a closed-loop, negative-feedback control system keeps the output voltage of the converter constant upon changing the operating conditions, i.e., the input voltage Vin and/or the output current lout thereof. This is achieved by comparing a portion of the output voltage to a reference voltage Vref. The difference, or error signal Er, between the value provided by the output voltage sensing system (usually, a resistor divider) and the reference value is amplified by an error amplifier. Its output Vc modifies a quantity x inside the converter which the energy carried by the converter during each switching cycle substantially depends on. As discussed above, such a significant quantity in resonant converters is the switching frequency of the square wave stimulating the resonant circuit.
As in all control systems in dc-dc converters, the frequency response of the error amplifier should be properly designed so as to ensure:                a stable control loop (i.e., that, upon disturbances of the operating conditions of the converter, once the transient caused by the disturbance has finished, the output voltage tends to recover a steady state value close to that before the disturbance;        good regulation (i.e., the new constant value recovered by the output voltage following a disturbance is very close to that preceding the perturbation);        good dynamic performance (i.e., during the transient following a disturbance, the output voltage does not excessively deviate from the desired value and the transient itself is short).        
The above-mentioned control objectives may be expressed in terms of some characteristic quantities of the transfer function of the control loop, such as the band width, the phase margin, the dc gain. In a dc-dc converter, these objectives may be achieved by acting on the frequency response of the error amplifier, modifying the gain thereof and conveniently placing the poles and zeroes of the transfer function thereof (frequency compensation). This is normally achieved by using passive networks comprising resistances and capacitors of appropriate value connected thereto.
However, in order to determine the frequency compensation used to obtain the desired features of the transfer function of the control loop, one should know both the modulator gain, i.e., the gain of the system converting the control voltage Vc into the control quantity x, and the frequency response of the converter itself to the variations of the quantity x.
The modulator gain does not usually depend on the frequency, and is fixed inside the control integrated circuit.
Although dc-dc converters are strongly non-linear system just because of the switching action, with suitable approximations and under certain hypothesis, their frequency response may be described and represented by the same means used for linear networks and, therefore, by a transfer function characterized by gain, zeroes and poles. This transfer function depends on the converter topology, i.e., the mutual configuration of the elements handling the power, on its operation mode, i.e., whether, at every switching cycle, there is a continuous current circulation in the magnetic part (Continuous Current Mode, CCM) or not (Discontinuous Current Mode, DCM), and on the quantity x controlled by the control loop. While in PWM converters different control methods are commonly used—traditionally, in resonant converters, the quantity used to control the converter is directly the switching frequency of the square wave applied to the resonant circuit.
In all integrated control circuits for dc-dc resonant converters available in the market, the control directly operates on the oscillation frequency of the half bridge (Direct Frequency Control, DFC). FIG. 2 shows a control system for this type of resonant converter. The output of the error amplifier 4 on the secondary side, having a part of the output voltage Vout at the input of the inverting terminal and a reference voltage Vref on the non-inverting terminal, is transferred to the primary side by an isolator 50, for example a photocoupler, so as to ensure the primary-secondary isolation required by the safety regulations, and acts upon a voltage-controlled oscillator (VCO) 6 or a current-controlled oscillator (ICO) inside the control integrated circuit 30.
This type of control arises two classes of problems. A first one relates to the fact that, unlike PWM converters, dynamic small-signal models for resonant converters expressed in terms of gain, poles and zeroes are not known in the literature (there are some approximated forms of questionable practical use). In other words, the transfer function of the power stage is not known. A second class of problems relates to the fact that, according to study results based on simulations, said transfer function of the power stage shows a strongly variable dc gain, and a number of poles varying from one to three and with a very mobile position, depending on the operating point. There is finally a zero due to the output capacitor.
The large gain variation and the highly variable pole configuration make the frequency compensation of the feedback control loop quite problematic. As a result, it is virtually impossible to obtain a transient response optimized under all the operating conditions, and a considerable trade-off between stability and dynamic performance occurs. Additionally, the energy transfer strongly depends on the input voltage (audio-susceptibility), so that the control loop has to significantly change the operating frequency to compensate said variations. Since in the input voltage of the converter there is an alternating component with a frequency twice that of the mains voltage, the loop gain at that frequency is quite high to effectively reject said alternating component and significantly attenuate the residual ripple visible in the output voltage.
All these factors risk to raise problems which may be not all solvable, especially when the load supplied by the converter has great dynamic changes and/or there are strict specifications on the dynamic accuracy, the response speed, or the rejection of the input ripple.
Finally, another problem related to the DFC control method is the sensitivity of the switching frequency to the value of the components in the resonant circuit (Cr, Ls and Lp). These values have a statistical spread due to their fabrication tolerances and this adversely affects the effectiveness of the protection circuits. In fact, generally speaking, to avoid that a converter may be operated abnormally, the control quantity x should be limited. In the case of resonant converters, the resonant controllers implementing DFC allow the operating frequency of the half bridge to be top and bottom limited. These limits should be set considering that, due to the above-mentioned value spread, the operating frequency range of the converter will change accordingly. The minimum limit set to the frequency should thus be lower than the minimum value which may be taken by the lower end of said range, and the maximum limit higher than the maximum value which may be taken by the higher end of said range. This significantly reduces the effectiveness of the frequency limitation as a means for preventing abnormal operational conditions.